Researchers often assess the relationship between an exposure and a composite endpoint comprising multiple distinct components. Components are often binary. Guidelines for choosing components call for similar severity, frequency (for binary) and treatment effect, which is rarely achieved. Thus, a key issue with standard analyses of binary-event composites is that highest frequency components dominate, even though often less serious. Mascha and Imrey (2010) introduced the average relative effect (ARE) GEE test since it averages distinct treatment effects across components, independent of their incidences, thus removing the tendency to overweight higher incident components. We extend this test to count data. Simulations and real data examples (Table 1) show that the extended ARE test for count data has better power than standard tests when components with smaller means are more affected. Power versus standard tests depends on heterogeneity of treatment effects, correlation among components, and marginal means (Figs 1, 2). The average relative effect test is particularly appropriate for the common situation when relative effects are at least as important as absolute effects.